However, the local topological order is still a useful indicator that we can still follow the similar result of the \(\mathbb {Z}_2\)  invariants [1]} to predict the number of Kramers pair edge states on an interface, \(N_K=\Delta \nu ~\mbox{mod}~2\) , where \(\Delta \nu \)  is the change in the local topological order across the interface.
For example, similar to the electronic topological insulator that a pair of edge states can exist on its outer boundary (i.e., interface between the nontrivial QSH material, \(\mathbb {Z}_2=1\) , and vacuum, \(\mathbb {Z}_2=0\) ), in the “zone-folding” system, a pair of band-gap-crossing edge states can be synthesised on an interface connecting two materials with \(\nu _1=+1/2\)  and \(\nu _2=-1/2\) .
At this point, given the sign of local topological order \(\nu \)  depends on the choice of the reference frame, it is natural to wonder if an edge state can exist on the interface between lattices having the same bulk pattern but with a relative translation (i.e., a dislocation interface).
The answer is indeed affirmative, and a way to conceive a pair of gapless pseudospin-polarized edge states on a dislocation interface is provided in Sec. .
